As far as AKC papers go, AKC will register a litter if all the paperwork is correct. They don't inspect the litters, so as long as mom and dad are registered, of the same breed and everything is signed, the "breeder" gets the litter registration.
Now, I am not saying you don't have the correct paperwork. You got the paperwork for a GSD, like the littermates. However, its very possible the dog is not purebred, but the breeders went ahead and registered all the pups, thinking this one was just small or possibly knew it was not purebred.
We had a nice sweet older puppy come into the vet clinic. It immediately looked to me like a Sheltie Doxy cross. Short legs, long back, longer coat, but a beautiful sheltie head/ears. In talking to the people, they stated that they were sold this puppy at 8 weeks as a registered Doxy, had the AKC papers, etc. As it grew, they realized it was no way purebred. They talked to the breeder and she stated" this puppy came from a registered dam and a registered sire, both Doxys. She even sent photos of the mom and dad tied during the breeding,, the litter from birth, growing up, etc. Their puppy has some unique markings that were there from birth. Yep, this was a registered Doxy. Of course, you could see in the photos a nice sable sheltie in the background. .
So, the bought an 8 week old registered Doxy puppy that was in fact half Sheltie, the sheltie was an intact male that ran with the rest of the dogs. She was a puppy mill of sorts.So, they did get back their money and love their little dog.
Its very possible and I suspect,that this breeder let the GSD female get bred, or maybe didn't even realize it got bred by something else and this little puppy was from the registered female, born at the same time as the true GSD littermates and the breeder just registered the whole litter, thinking (or knowing it wasn't)it was purebred because it was black/tan like the rest of the litter, just smaller.
Not sure if you vet will be able to do much except helping you decide what this puppy is, if it isn't purebred. You will have to contact the pet shop and breeder with your doubts and push to find out if this puppy is indeed purebred and either small or has some genetic issues, or is a mix and you need to get your money back. At this point, the AKC papers show it is purebred, but unless you are able to DNA the whole litter and both parents to see if your pup is sharing the same DNA, not much you can do.
A DNA test can give mix results from just sending in your pups DNA, but the whole litter or at least testing a littermate or two and both parents will give you the true story.